{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "20d1844d-56a1-4d97-9098-04cd38614402",
   "metadata": {},
   "source": [
    "# Using time to model a non-linear trend"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c7e22b9-366f-4754-ba9c-c642f5b6f291",
   "metadata": {},
   "source": [
    "[Feature Engineering for Time Series Forecasting](https://www.trainindata.com/p/feature-engineering-for-forecasting)\n",
    "\n",
    "In this notebook we show how to create a feature using time to capture the trend of a time series. We'll look at using powers of the time feature to create non-linear trends. We will use it to create some simple forecasts with a linear regression. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9a86e7d9-212c-4d82-b896-20a4e078c336",
   "metadata": {},
   "outputs": [],
   "source": [
    "import datetime\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_context(\"talk\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c51d42e9-8edd-416d-8ac1-9a77792a9ed8",
   "metadata": {},
   "source": [
    "# Data set synopsis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e964ccb-f3fd-4e88-a08a-b82e6fc56074",
   "metadata": {},
   "source": [
    "The air passengers dataset is the monthly totals of international airline passengers, from 1949 to 1960, in units of 1000s. \n",
    "\n",
    "For instructions on how to download, prepare, and store the dataset, refer to notebook number 5, in the folder \"01-Create-Datasets\" from this repo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0b41fdf4-7f04-4fa6-ae61-5831d3b36473",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\n",
    "    \"../Datasets/example_air_passengers.csv\",\n",
    "    parse_dates=[\"ds\"],\n",
    "    index_col=[\"ds\"],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e615ae1-842c-4aae-bb2a-75d13e07ff3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ds</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              y\n",
       "ds             \n",
       "1949-01-01  112\n",
       "1949-02-01  118\n",
       "1949-03-01  132\n",
       "1949-04-01  129\n",
       "1949-05-01  121"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea3cc441-df77-439b-a88d-e74c334635c3",
   "metadata": {},
   "source": [
    "## Plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e096e012-faba-477d-b0b3-6d2a2aac6407",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=[10, 5])\n",
    "data.plot(y=\"y\", marker=\".\", figsize=[10, 5], legend=None, ax=ax)\n",
    "ax.set_xlabel(\"Time\")\n",
    "ax.set_ylabel(\"Air passengers (1000s)\")\n",
    "ax.set_title(\"Air passenger numbers\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b6726d8-7d4c-4b21-b532-6b53a8e3d0d1",
   "metadata": {},
   "source": [
    "# Let's create non-linear time features"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed11084b-3ed2-4353-b25e-bd0141fc22f6",
   "metadata": {},
   "source": [
    "Let's see how we can create these features with higher order terms such as $t^2$, $t^3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "130d5c18-2870-4a1a-89af-c09bdff6b775",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new copy of the original data.\n",
    "df = data.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a397abf0-8919-4e60-a7cb-693eec2514ec",
   "metadata": {},
   "source": [
    "Create the time feature (i.e., the time since the start of the time series)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ecec5827-6bb4-474c-a3e8-e76193f139f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Requires version 0.14.1 or greater of sktime.\n",
    "from sktime.transformations.series.time_since import TimeSince"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b467276b-034f-4a71-b38d-794d60355660",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>time_since_1949-01-01 00:00:00</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ds</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              y  time_since_1949-01-01 00:00:00\n",
       "ds                                             \n",
       "1949-01-01  112                               0\n",
       "1949-02-01  118                               1\n",
       "1949-03-01  132                               2\n",
       "1949-04-01  129                               3\n",
       "1949-05-01  121                               4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time_since_transformer = TimeSince(keep_original_columns=True, freq=\"MS\")\n",
    "\n",
    "# Compute the time since the start of the time series\n",
    "df = time_since_transformer.fit_transform(df)\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8958d891-6135-4abc-978c-0ac11f10c6a5",
   "metadata": {},
   "source": [
    "We could manually create these features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7ae0c8f1-6011-47df-ad3b-415037119362",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>time_since_1949-01-01 00:00:00</th>\n",
       "      <th>t^2</th>\n",
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       "    <tr>\n",
       "      <th>ds</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121</td>\n",
       "      <td>4</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              y  time_since_1949-01-01 00:00:00  t^2\n",
       "ds                                                  \n",
       "1949-01-01  112                               0    0\n",
       "1949-02-01  118                               1    1\n",
       "1949-03-01  132                               2    4\n",
       "1949-04-01  129                               3    9\n",
       "1949-05-01  121                               4   16"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"t^2\"] = df[\"time_since_1949-01-01 00:00:00\"] ** 2\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d71d1bfa-3305-4527-8c23-7d7e62715956",
   "metadata": {},
   "source": [
    "Alternatively, here is an example using the `PolynomialFeatures` transformer. By specifying `degree`, $d$, the transformer will output the following columns: $t$, $t^2$, ..., $t^d$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1fb5382c-5c8b-4ebf-a7da-f7d058d6ab71",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's ensure all sklearn transformers output pandas dataframes\n",
    "from sklearn import set_config\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "set_config(transform_output=\"pandas\")  # Upgrade to scikit-learn 0.12\n",
    "                                       # for this feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1f0bc188-015b-48d4-8ca1-89404cc22098",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time_since_1949-01-01 00:00:00</th>\n",
       "      <th>time_since_1949-01-01 00:00:00^2</th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>4.0</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>139.0</td>\n",
       "      <td>19321.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>140.0</td>\n",
       "      <td>19600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>141.0</td>\n",
       "      <td>19881.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>142.0</td>\n",
       "      <td>20164.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>143.0</td>\n",
       "      <td>20449.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>144 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            time_since_1949-01-01 00:00:00  time_since_1949-01-01 00:00:00^2\n",
       "ds                                                                          \n",
       "1949-01-01                             0.0                               0.0\n",
       "1949-02-01                             1.0                               1.0\n",
       "1949-03-01                             2.0                               4.0\n",
       "1949-04-01                             3.0                               9.0\n",
       "1949-05-01                             4.0                              16.0\n",
       "...                                    ...                               ...\n",
       "1960-08-01                           139.0                           19321.0\n",
       "1960-09-01                           140.0                           19600.0\n",
       "1960-10-01                           141.0                           19881.0\n",
       "1960-11-01                           142.0                           20164.0\n",
       "1960-12-01                           143.0                           20449.0\n",
       "\n",
       "[144 rows x 2 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create and use the polynomial transformer.\n",
    "poly_transformer = PolynomialFeatures(\n",
    "    degree=2, # degree of polynomial\n",
    "    include_bias=False  # exclude constant term\n",
    ")\n",
    "\n",
    "# Create polynomial features from a given column\n",
    "result = poly_transformer.fit_transform(df[[\"time_since_1949-01-01 00:00:00\"]])\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "738fef10-97fd-4e1b-90c6-148844979cd8",
   "metadata": {},
   "source": [
    "Let's create a single transformer that outputs our polynomial features for time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0c53567d-2263-4d04-b203-7e0fb576e5e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d7b5c3b8-2411-4026-83c8-eb1ae22b1e26",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_feats = make_pipeline(\n",
    "                           TimeSince(freq=\"MS\"), \n",
    "                           PolynomialFeatures(degree=2, include_bias=False)\n",
    "                          )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7a566b31-3834-41d2-8bb5-c4fe2fe608f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new copy of the original data.\n",
    "df = data.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8e34236e-83e9-4854-af70-75d9e3a5f707",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time_since_1949-01-01 00:00:00</th>\n",
       "      <th>time_since_1949-01-01 00:00:00^2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ds</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>4.0</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>139.0</td>\n",
       "      <td>19321.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>140.0</td>\n",
       "      <td>19600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>141.0</td>\n",
       "      <td>19881.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>142.0</td>\n",
       "      <td>20164.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>143.0</td>\n",
       "      <td>20449.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>144 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            time_since_1949-01-01 00:00:00  time_since_1949-01-01 00:00:00^2\n",
       "ds                                                                          \n",
       "1949-01-01                             0.0                               0.0\n",
       "1949-02-01                             1.0                               1.0\n",
       "1949-03-01                             2.0                               4.0\n",
       "1949-04-01                             3.0                               9.0\n",
       "1949-05-01                             4.0                              16.0\n",
       "...                                    ...                               ...\n",
       "1960-08-01                           139.0                           19321.0\n",
       "1960-09-01                           140.0                           19600.0\n",
       "1960-10-01                           141.0                           19881.0\n",
       "1960-11-01                           142.0                           20164.0\n",
       "1960-12-01                           143.0                           20449.0\n",
       "\n",
       "[144 rows x 2 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = time_feats.fit_transform(df)\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b37cb4-3d4a-41e8-9d03-4ed219d57d4a",
   "metadata": {},
   "source": [
    "# Let's build a forecast with just these non-linear time features."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee379cf9-1895-4505-ae22-70ee155f1363",
   "metadata": {},
   "source": [
    "As with the previous notebook, in this notebook we will focus more on the impact of these features rather than the overall forecasting workflow. We will show the creation of these features in a recursive forecasting workflow in the next notebook. We will see what impact using higher order terms such as $t^2$, $t^3$, and so on can have."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "06544908-62a8-435f-b287-9baec22229d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new copy of the original data.\n",
    "df = data.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57cf9f07-22d7-4c46-a149-775524907a0b",
   "metadata": {},
   "source": [
    "Let's split the data into train and test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7426628a-c089-47ed-b3ae-780abb1f49e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "target = \"y\"\n",
    "holdout_size = 12 * 6  # forecast horizon\n",
    "\n",
    "# Use all the time up until the start\n",
    "# of the forecast horizon for training.\n",
    "df_train = df.iloc[:-holdout_size]\n",
    "\n",
    "# Use the end of the time series\n",
    "# to test.\n",
    "df_test = df.iloc[-holdout_size:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "939d50b5-c51c-4aff-a8e3-81a7d085c187",
   "metadata": {},
   "source": [
    "Create our feature engineering pipeline. Ridge and Lasso require feature scaling. Let's scale the features as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "796ea887-3244-4af3-ba82-229503a6c0e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import MinMaxScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e32b2857-f520-4fc5-b585-f023e1ac5158",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify degree of polynomial\n",
    "degree = 3\n",
    "\n",
    "time_feats = make_pipeline(\n",
    "                            TimeSince(freq=\"MS\"),\n",
    "                            PolynomialFeatures(degree=degree, include_bias=False),\n",
    "                            MinMaxScaler()\n",
    "                          )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47d141a8-4679-4d3a-94a7-7538e949fb7a",
   "metadata": {},
   "source": [
    "Create X and y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7b37933c-807e-4deb-8cb9-1d08c724854c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time_since_1949-01-01 00:00:00</th>\n",
       "      <th>time_since_1949-01-01 00:00:00^2</th>\n",
       "      <th>time_since_1949-01-01 00:00:00^3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ds</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1955-01-01</th>\n",
       "      <td>1.014085</td>\n",
       "      <td>1.028367</td>\n",
       "      <td>1.042851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-02-01</th>\n",
       "      <td>1.028169</td>\n",
       "      <td>1.057132</td>\n",
       "      <td>1.086910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-03-01</th>\n",
       "      <td>1.042254</td>\n",
       "      <td>1.086292</td>\n",
       "      <td>1.132192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-04-01</th>\n",
       "      <td>1.056338</td>\n",
       "      <td>1.115850</td>\n",
       "      <td>1.178715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-05-01</th>\n",
       "      <td>1.070423</td>\n",
       "      <td>1.145804</td>\n",
       "      <td>1.226495</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            time_since_1949-01-01 00:00:00  time_since_1949-01-01 00:00:00^2  \\\n",
       "ds                                                                             \n",
       "1955-01-01                        1.014085                          1.028367   \n",
       "1955-02-01                        1.028169                          1.057132   \n",
       "1955-03-01                        1.042254                          1.086292   \n",
       "1955-04-01                        1.056338                          1.115850   \n",
       "1955-05-01                        1.070423                          1.145804   \n",
       "\n",
       "            time_since_1949-01-01 00:00:00^3  \n",
       "ds                                            \n",
       "1955-01-01                          1.042851  \n",
       "1955-02-01                          1.086910  \n",
       "1955-03-01                          1.132192  \n",
       "1955-04-01                          1.178715  \n",
       "1955-05-01                          1.226495  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train = time_feats.fit_transform(df_train)\n",
    "y_train = df_train[target]\n",
    "\n",
    "X_test = time_feats.transform(df_test)\n",
    "y_test = df_test[target]\n",
    "\n",
    "X_test.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2c1745f-b1d4-4b28-94ac-1923f58a584f",
   "metadata": {},
   "source": [
    "Build forecast. We have all the features in both train and test, we're not building features from the target variable. So we're not using either direct or recursive forecasting for multi-step forecasting here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e31b71ef-e04e-4fc4-b919-aa0f08979097",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso, LinearRegression, Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d8b9229a-9a91-4fbd-8ca9-aa8d45b98144",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the model.\n",
    "model = LinearRegression()\n",
    "\n",
    "# Fit model.\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "# Make forecast and convert to dataframes.\n",
    "y_pred_train = model.predict(X_train)\n",
    "y_pred_train = pd.DataFrame(y_pred_train, index=df_train.index)\n",
    "\n",
    "y_pred_test = model.predict(X_test)\n",
    "y_pred_test = pd.DataFrame(y_pred_test, index=df_test.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "12749bc8-399e-4a04-bbbd-4626eb9ab73a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=[10, 5])\n",
    "\n",
    "df_train[target].plot(ax=ax, marker=\".\")\n",
    "df_test[target].plot(ax=ax, marker=\".\", color=\"r\", alpha=0.4)\n",
    "\n",
    "y_pred_train.plot(color=\"k\", ax=ax)\n",
    "y_pred_test.plot(color=\"k\", ax=ax, linestyle=\"--\")\n",
    "\n",
    "ax.legend([\"train\", \"test\", \"y_pred train set\", \"y_pred test set\"])\n",
    "ax.set_xlabel(\"Time\")\n",
    "ax.set_ylabel(\"Air passengers\")\n",
    "ax.set_title(\"Air passengers\")\n",
    "ax.ticklabel_format(style=\"sci\", axis=\"y\", scilimits=(0, 0))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "41c6bc9b-cfb1-4650-84dc-7b4433559a14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "time_since_1949-01-01 00:00:00       -2.679744\n",
       "time_since_1949-01-01 00:00:00^2    363.302794\n",
       "time_since_1949-01-01 00:00:00^3   -243.127004\n",
       "dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Examine model coefficients.\n",
    "pd.Series(index=X_train.columns, data=model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "729fb5c9-7350-49ee-bcb9-7733744b8866",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22.864911883894223\n",
      "419.58053886187\n"
     ]
    }
   ],
   "source": [
    "# Compute error metrics.\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "print(mean_squared_error(df_train[target], y_pred_train, squared=False))\n",
    "print(mean_squared_error(df_test[target], y_pred_test, squared=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eae36ced-7ecd-42d6-9902-4220f899960c",
   "metadata": {},
   "source": [
    "In general, it is not recommended to use $t^2$ terms or higher. But, we can see that regularisation can help. In practice, it's best to experiment and see which features produce the best forecast for your own use case."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a852588-8ce9-488b-ad52-655a081a8735",
   "metadata": {},
   "source": [
    "In the next notebook we'll show how the time feature helps in addition to adding lag features in a more complex example where we will use recursive forecasting."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
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   "title_cell": "Table of Contents",
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